Lecture 2Lecture 2

Robert ZimmerRobert Zimmer

Room 6, 25 St JamesRoom 6, 25 St James

This course is about building This course is about building models and making decisionsmodels and making decisions

► It is about organising informationIt is about organising information► It is about being able to ask what-if It is about being able to ask what-if

questionsquestions► It is about applying powerful It is about applying powerful

mathematical models (I might try to mathematical models (I might try to teach you some maths when you teach you some maths when you aren’t looking but that is incidental)aren’t looking but that is incidental)

Example of a decision:Example of a decision:should I have another beer?should I have another beer?

►Organising Information:Organising Information: How much money I haveHow much money I have How much money a beer costsHow much money a beer costs How drunk am I? How drunk am I? Do I have to drive?Do I have to drive? How fat am I?How fat am I? How much do I like the people in the pub?How much do I like the people in the pub? How much do I like the people at home?How much do I like the people at home?

Another QuestionAnother Question

►What is the most money I am What is the most money I am prepared to pay for this drink? That is prepared to pay for this drink? That is at what price does the pleasure of the at what price does the pleasure of the drink become less than its price?drink become less than its price?

Some more questionsSome more questions

►What is the geometric shape of all the What is the geometric shape of all the points at which the pleasure of the points at which the pleasure of the beer exactly matches the pain of the beer exactly matches the pain of the payment? payment?

►How will my pleasure, my weight, and How will my pleasure, my weight, and my mental state compare if instead of my mental state compare if instead of a beer I have chips? a beer I have chips?

►or do my Java coursework?or do my Java coursework?

► Spreadsheet modelingSpreadsheet modeling is the process of is the process of

entering the inputs and decision variables into a entering the inputs and decision variables into a spreadsheet and then relating them spreadsheet and then relating them appropriately, by means of formulas, to obtain the appropriately, by means of formulas, to obtain the outputs.outputs.

►Once a model is created there are several Once a model is created there are several directions in which to proceed.directions in which to proceed. Sensitivity analysis to see how one or more outputs Sensitivity analysis to see how one or more outputs

change as selected inputs or decision variables change.change as selected inputs or decision variables change. Finding the value of a decision variable that maximizes Finding the value of a decision variable that maximizes

or minimizes a particular output.or minimizes a particular output. Create graphs to show graphically how certain Create graphs to show graphically how certain

parameters of the model are related.parameters of the model are related.

►Good spreadsheet modeling practices are Good spreadsheet modeling practices are essential.essential.

► Spreadsheet models should be designed with Spreadsheet models should be designed with readability in mind.readability in mind.

► Several features that improve readability Several features that improve readability include:include:

►A clear logical layout to the overall modelA clear logical layout to the overall model►Separation of different parts of a modelSeparation of different parts of a model►Clear headings for different sections of the model Clear headings for different sections of the model ►Liberal use of range namesLiberal use of range names►Liberal use of formatting featuresLiberal use of formatting features►Liberal use of cell commentsLiberal use of cell comments►Liberal use of text boxes for assumptions, lists or Liberal use of text boxes for assumptions, lists or

explanationsexplanations

Example 2.1 – Building a Example 2.1 – Building a ModelModel

► Randy Kitchell is a NCAA t-shirt vendor. Randy Kitchell is a NCAA t-shirt vendor. The fixed cost of any order is $750, the The fixed cost of any order is $750, the variable cost is $6 per shirt. variable cost is $6 per shirt.

► Randy’s selling price is $10 per shirt, Randy’s selling price is $10 per shirt, until a week after the tournament when until a week after the tournament when it will drop to $4 apiece. The expected it will drop to $4 apiece. The expected demand at full price is 1500 shirts.demand at full price is 1500 shirts.

►He wants to build a spreadsheet model He wants to build a spreadsheet model that will let him experiment with the that will let him experiment with the uncertain demand and his order quantity.uncertain demand and his order quantity.

►In this model the profit is calculated with the formula

Profit = Revenue – Cost and the Cost = 750 + 6*B4

RevenueRevenue

Case 1: Demand outstrips order (B3 > B4)In that case everything gets sold for 10

dollars Revenue is then simply 10*B4(since B4 is the number ordered)

RevenueRevenue

Case 2:You have ordered too many.That is order (B3) is less than peak

demandThen you can only sell B3 at 10 dollars

and the rest (B4-B3) at 4 dollars

Revenue = 10*B3+4*(B4-B3)

Revenue FormulaRevenue Formula

Revenue = Revenue =

IF(B3>B4,10*B4,10*B3+4*(B4-B3))

Profit FormulaProfit Formula

Profit = Profit =

IF(B3>B4,10*B4,10*B3+4*(B4-B3)) – (750 + 6* B4)

Adding FlexibilityAdding Flexibility

►We add flexibility by allowing more We add flexibility by allowing more things to varythings to vary

Ex. 2.1(cont’d) - Building a Ex. 2.1(cont’d) - Building a ModelModel

► The formula can be rewritten to be more flexible.The formula can be rewritten to be more flexible.=-B3-B4*B9+IF(B8>B9,10*B8+B6*(B9-B8))=-B3-B4*B9+IF(B8>B9,10*B8+B6*(B9-B8))

► It can be made more readable by using range It can be made more readable by using range names. The formula would then readnames. The formula would then read=-Fixed_order_cost-Variable_cost*Order + =-Fixed_order_cost-Variable_cost*Order + IF(Demand > Order, Selling_price*Order, IF(Demand > Order, Selling_price*Order, 10*Demand+Salvage_value* (Order-Demand)10*Demand+Salvage_value* (Order-Demand)

Ex. 2.1(cont’d) - Building a Ex. 2.1(cont’d) - Building a ModelModel

►We might like to have profit broken down We might like to have profit broken down into various costs and revenues, rather one into various costs and revenues, rather one single profit cell. The profit formula would be single profit cell. The profit formula would be

= -(B12+B13)+(B15+B16).= -(B12+B13)+(B15+B16).► Range names could be used for these Range names could be used for these

intermediate output cells, but it is probably intermediate output cells, but it is probably more work than it is worth.more work than it is worth.

► Labels and/or color coding can help a lot Labels and/or color coding can help a lot with readability. with readability.

Ex. 2.1(cont’d) - Building a Ex. 2.1(cont’d) - Building a ModelModel

►Data tables could be used to see how sensitive Data tables could be used to see how sensitive profit is to the inputs, the demand, and the order profit is to the inputs, the demand, and the order quantity, and charts to show any numerical quantity, and charts to show any numerical results graphically.results graphically.

Example 2.2 – Cost Example 2.2 – Cost ProjectionsProjections

► The company knows that wood prices and The company knows that wood prices and labor costs are likely to increase in the future, labor costs are likely to increase in the future, and it would like to project its costs of and it would like to project its costs of manufacturing the bookshelves into the future.manufacturing the bookshelves into the future.

► The data can be found in Table 2.1.The data can be found in Table 2.1.► Build a spreadsheet model that allows the Build a spreadsheet model that allows the

company to experiment with the growth rates company to experiment with the growth rates in wood and labor costs so that a manager can in wood and labor costs so that a manager can see, both numerically and graphically, how the see, both numerically and graphically, how the costs of the bookshelves will vary in the next costs of the bookshelves will vary in the next few years.few years.

Ex. 2.2(cont’d) - Planning the Ex. 2.2(cont’d) - Planning the ModelModel

► The reasoning behind the model is The reasoning behind the model is straightforward.straightforward.

► First project the unit costs for wood and First project the unit costs for wood and labor into the future. Then for any year, labor into the future. Then for any year, multiply the unit costs by the required multiply the unit costs by the required numbers of board-feet and labor hours numbers of board-feet and labor hours per bookshelf.per bookshelf.

► Finally, add the wood ad labor costs to Finally, add the wood ad labor costs to obtain the total cost of a bookshelf.obtain the total cost of a bookshelf.

Ex. 2.2(cont’d) – The ModelEx. 2.2(cont’d) – The Model

Ex. 2.2(cont’d) – Developing the Ex. 2.2(cont’d) – Developing the Model Model

►Develop the model with the following steps.Develop the model with the following steps. Inputs: Inputs: Enter the inputs into the upper left Enter the inputs into the upper left

corner of a worksheet. These can be referred to corner of a worksheet. These can be referred to later with Excel formulas.later with Excel formulas.

Design output table:Design output table: You need to think ahead You need to think ahead of time how you want to structure your outputs. of time how you want to structure your outputs. The important point is that you should have The important point is that you should have some logical design in mind before diving in.some logical design in mind before diving in.

Projected unit costs of wood:Projected unit costs of wood: It is important It is important to have a strategy in mind before you enter the to have a strategy in mind before you enter the formulas. You should design your spreadsheet formulas. You should design your spreadsheet so that you can enter a single formula and then so that you can enter a single formula and then copy it whenever possible. copy it whenever possible.

Ex. 2.2(cont’d) – Developing the Ex. 2.2(cont’d) – Developing the ModelModel

► For example: enter the formula For example: enter the formula =B9=B9 in cell B19 and copy it in cell B19 and copy it to cell C19. Then enter the general formula to cell C19. Then enter the general formula =B19*(1+B$10)=B19*(1+B$10) in cell B20 and copy it to the range in cell B20 and copy it to the range B20:C25.B20:C25.

4.4. Projected unit labor costs:Projected unit labor costs: To calculate projected To calculate projected hourly labor costs, enter the formula hourly labor costs, enter the formula =B13=B13 in cell in cell D19. Then enter the formula D19. Then enter the formula =D19*(1+B$14)=D19*(1+B$14) in cell in cell D20 and copy it down to column D.D20 and copy it down to column D.

5.5. Projected bookshelf costs:Projected bookshelf costs: With careful use of With careful use of absolute and relative addresses, enter a single absolute and relative addresses, enter a single formula for these costs – for all years and for both formula for these costs – for all years and for both types of wood. To do this, enter the formula types of wood. To do this, enter the formula =B$5*B19+B$6*$D19=B$5*B19+B$6*$D19 in cell E19 and copy it to the in cell E19 and copy it to the range E19:F25.range E19:F25.

Developing the Model -- Developing the Model -- continuedcontinued

6.6. Chart:Chart: Highlight the range E19:F25 and click on Highlight the range E19:F25 and click on Excel’s Chart Wizard button. This leads you Excel’s Chart Wizard button. This leads you through a sequence of steps. You should through a sequence of steps. You should experiment with the possibilities. experiment with the possibilities.

► The model can be used to answer any what-if The model can be used to answer any what-if questions Woodworks might want to ask.questions Woodworks might want to ask.

► The model has been built in such a way that a The model has been built in such a way that a manager can enter any desired values in the manager can enter any desired values in the input cells, and all of the outputs , including input cells, and all of the outputs , including the chart, will update automatically.the chart, will update automatically.

► Burying input numbers inside Excel formulas Burying input numbers inside Excel formulas is bad practice.is bad practice.

2.4 Breakeven Analysis2.4 Breakeven Analysis

►Many business problems require us to Many business problems require us to find the appropriate level of some find the appropriate level of some activity.activity.

►This might be the level that maximizes This might be the level that maximizes profit, or it might be the level that profit, or it might be the level that allows a company to break even – no allows a company to break even – no profit, no loss.profit, no loss.

Example 2.3 - Breakeven Example 2.3 - Breakeven AnalysisAnalysis► The Great Threads Company is planning to The Great Threads Company is planning to

print a brochure of its products and print a brochure of its products and undertake a direct mail campaign.undertake a direct mail campaign.

► The cost of printing the brochure is The cost of printing the brochure is $20,000 plus $0.10 a catalog. The cost of $20,000 plus $0.10 a catalog. The cost of mailing each catalog is $0.15. In addition, mailing each catalog is $0.15. In addition, the company will include direct reply the company will include direct reply envelopes in it’s mailings. It incurs $0.20 envelopes in it’s mailings. It incurs $0.20 in extra cost for each direct mail envelope in extra cost for each direct mail envelope that is used by a respondent.that is used by a respondent.

► The average size of a customer order is The average size of a customer order is $40, and the company’s variable cost per $40, and the company’s variable cost per order averages around 80% of the order’s order averages around 80% of the order’s value.value.

Ex. 2.3(cont’d) - Breakeven Ex. 2.3(cont’d) - Breakeven AnalysisAnalysis

► The company plans to mail 100,000 The company plans to mail 100,000 catalogs. It wants to develop a spreadsheet catalogs. It wants to develop a spreadsheet model to answer the following questions:model to answer the following questions: How does a change in the response rate affect How does a change in the response rate affect

profit?profit? For what response rate does a company break For what response rate does a company break

even?even? If the company estimates a response rate of 3%, If the company estimates a response rate of 3%,

should it proceed with the mailing?should it proceed with the mailing? How does the presence of uncertainty affect the How does the presence of uncertainty affect the

usefulness of the model?usefulness of the model?

Ex. 2.3(cont’d) - Planning the Ex. 2.3(cont’d) - Planning the ModelModel

► A single “bottom line” output variable, in A single “bottom line” output variable, in this case profit, is of most concern.this case profit, is of most concern.

► The logic for converting inputs and the The logic for converting inputs and the decision variable into outputs is quite decision variable into outputs is quite straightforward. Then it must be straightforward. Then it must be investigated how the response rate affects investigated how the response rate affects the profit with a sensitivity analysis.the profit with a sensitivity analysis.

Ex. 2.3(cont’d) - Developing the Ex. 2.3(cont’d) - Developing the ModelModel

► To create this model, proceed through the To create this model, proceed through the following steps.following steps.1.1. Heading and range names:Heading and range names: Be cautious not to Be cautious not to

go overboard with range names.go overboard with range names.2.2. Enter input values: Enter input values: Some of the values have Some of the values have

been combined in the statement of the problem. been combined in the statement of the problem. To document this process, enter comments in a To document this process, enter comments in a few cells. Inserting comments in cells is a great few cells. Inserting comments in cells is a great way to document your spreadsheet models without way to document your spreadsheet models without making it too cluttered.making it too cluttered.

3.3. Model the responses:Model the responses: Enter any reasonable Enter any reasonable value, such as 8%, in the Respone_rate cell. value, such as 8%, in the Respone_rate cell. ==Number_mailed*Response_rateNumber_mailed*Response_rate in cell E5 in cell E5

Ex. 2.3(cont’d) - Developing Ex. 2.3(cont’d) - Developing the Modelthe Model

4.4. Model the revenues, costs and profits:Model the revenues, costs and profits:► Enter the formula Enter the formula

=Number_of_responses*Average_order=Number_of_responses*Average_order in the in in the in cell E8.cell E8.

► Enter the formula Enter the formula =Fixed_cost_of_printing=Fixed_cost_of_printing, , =Variable_cost_of_printing_mailing*Number_mail=Variable_cost_of_printing_mailing*Number_mailed ed and and =Number_of_responses*Variable_cost_per_order =Number_of_responses*Variable_cost_per_order in cells E9, E10, and E11.in cells E9, E10, and E11.

► Enter the formula Enter the formula =SUM(E9:E11)=SUM(E9:E11) in the cell E12, and in the cell E12, and enter the formula enter the formula =Total_revenue-Total_cost =Total_revenue-Total_cost in the in the cell E13.cell E13.

Ex. 2.3(cont’d) - Data TableEx. 2.3(cont’d) - Data Table► A a one-way data table is formed to show A a one-way data table is formed to show

how profit varies with the response rate.how profit varies with the response rate.► Data tables are called “what-if” tables. They Data tables are called “what-if” tables. They

illustrate what happens to selected outputs if illustrate what happens to selected outputs if selected inputs change.selected inputs change.

► From the data table it can be seen that profit From the data table it can be seen that profit changes from negative to positive when the changes from negative to positive when the response rate is somewhere between 5% response rate is somewhere between 5% and 6%.and 6%.

► This could be found by trial and error, but it This could be found by trial and error, but it is easier to find with Excel’s Goal Seek tool.is easier to find with Excel’s Goal Seek tool.

Ex. 2.3(cont’d) - Goal SeekEx. 2.3(cont’d) - Goal Seek

►Goal seek is useful for solving a Goal seek is useful for solving a singlesingle equation in a equation in a singlesingle unknown. unknown.

►The unknown is called the The unknown is called the changing changing cellcell because it is allowed to be because it is allowed to be changed to make the equation true.changed to make the equation true.

►Select the Tools/Goal Seek menu item Select the Tools/Goal Seek menu item and fill in the resulting dialog box.and fill in the resulting dialog box.

► If the response rate is 5.77%, Great If the response rate is 5.77%, Great Threads breaks even.Threads breaks even.

Ex. 2.3(cont’d) - Limitations of Ex. 2.3(cont’d) - Limitations of the Modelthe Model

►Question 3 asks whether the company Question 3 asks whether the company should proceed with the mailing if the should proceed with the mailing if the response rate is only 3%. response rate is only 3%.

► The apparent answer is “no” because profit The apparent answer is “no” because profit is negative. This reasoning is taking the is negative. This reasoning is taking the short-term view.short-term view.

► To consider the long term impact of our To consider the long term impact of our decisions the model must incorporate the decisions the model must incorporate the long term explicitly into the model. To do long term explicitly into the model. To do this a more complex model must be built.this a more complex model must be built.

Ex. 2.3(cont’d) - Ex. 2.3(cont’d) - Limitations of the ModelLimitations of the Model

►Question 4 asks about the impact Question 4 asks about the impact of uncertainty in the model. of uncertainty in the model.

► It makes more sense to talk about It makes more sense to talk about the the probabilityprobability that profit will have that profit will have a certain value or the a certain value or the probabilityprobability that the company will break even.that the company will break even.

2.6 Decisions Involving the Time 2.6 Decisions Involving the Time Value of MoneyValue of Money

► Cash flows are received at different points in Cash flows are received at different points in time, and a company must determine a course time, and a company must determine a course of action that maximizes the “value” of cash of action that maximizes the “value” of cash flows.flows.

► The later a dollar is received, the less valuable The later a dollar is received, the less valuable the dollar is. This is useful in making decisions.the dollar is. This is useful in making decisions.

$1.00 X 1/(1+$1.00 X 1/(1+rr) now = $1.00 a year from ) now = $1.00 a year from nownow

► The value 1/(1+r) in the above equation is The value 1/(1+r) in the above equation is called the called the discount factordiscount factor..

► The quantity on the left is called the The quantity on the left is called the present present

valuevalue of $1.00 received a year from now. of $1.00 received a year from now.► If money can be invested at annual rate If money can be invested at annual rate rr

compounded each year, then $1 received compounded each year, then $1 received tt years years from now has the same value as 1/(1+r)from now has the same value as 1/(1+r)tt dollars dollars received today – that is, the $1 is discounted by received today – that is, the $1 is discounted by the discount factor raised to the the discount factor raised to the tt power. power.

► By multiplying a cash flow received By multiplying a cash flow received tt years from years from now by 1/(1+now by 1/(1+rr))tt (its present value), then the total (its present value), then the total value of all cash flows over all years is called the value of all cash flows over all years is called the net present value (NPV) of our cash flows.net present value (NPV) of our cash flows.

►The rate The rate r r (usually called the (usually called the discount discount raterate) used by major corporations ) used by major corporations generally comes from some version of generally comes from some version of the the capital asset pricing model.capital asset pricing model.

►The The discount factordiscount factor is 1 divided by 1 is 1 divided by 1 plus the plus the discount ratediscount rate..

►The The NPVNPV is the sum of all discounted is the sum of all discounted cash flows.cash flows.